Razumikhin-type theorems on exponential stability of stochastic functional differential equations

Research output: Contribution to journalArticle

139 Citations (Scopus)

Abstract

Although the Razumikhin-type theorems have been well developed for the stability of functional differential equations and they are very useful in applications, so far there is almost no result of Razumikhin type on the stability of stochastic functional differential equations. The main aim of this paper is to close this gap by establishing several Razumikhin-type theorems on the exponential stability for stochastic functional differential equations. By applying these new results to stochastic differential delay equations and stochastically perturbed equations we improve or generalize several known results, and this shows the powerfulness of our new results clearly.

LanguageEnglish
Pages233-250
Number of pages18
JournalStochastic Processes and their Applications
Volume65
Issue number2
DOIs
Publication statusPublished - 27 Dec 1996

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Stochastic Functional Differential Equations
Exponential Stability
Asymptotic stability
Differential equations
Theorem
Stochastic Differential Delay Equations
Functional Differential Equations
Generalise
Exponential stability

Keywords

  • Borel-Cantelli lemma
  • Brownian motion
  • Burkholder-davis-gundy's inequality
  • Lyapunov exponent
  • Razumikhin theorem

Cite this

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abstract = "Although the Razumikhin-type theorems have been well developed for the stability of functional differential equations and they are very useful in applications, so far there is almost no result of Razumikhin type on the stability of stochastic functional differential equations. The main aim of this paper is to close this gap by establishing several Razumikhin-type theorems on the exponential stability for stochastic functional differential equations. By applying these new results to stochastic differential delay equations and stochastically perturbed equations we improve or generalize several known results, and this shows the powerfulness of our new results clearly.",
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Razumikhin-type theorems on exponential stability of stochastic functional differential equations. / Mao, Xuerong.

In: Stochastic Processes and their Applications, Vol. 65, No. 2, 27.12.1996, p. 233-250.

Research output: Contribution to journalArticle

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